What is the term for the soft part that finally becomes the core of a tree?

Sapwood is the term for the soft part that finally becomes the core of a tree.

Specifically, sapwood can be found between the cambium cell layer and the heartwood. It functions to transport water into the tree's foliage. It is made up of layers of newer and older wood. The older wood will harden into heartwood as newer layers are added. It therefore will turn into the core of a tree over time and with age.